Application of a momentum-space semi-locally regularized chiral potential to selected disintegration processes

We apply a recently developed momentum-space semilocally regularized chiral potential to the ${}^2\mathrm{H}$ and ${}^3\mathrm{He}$ photodisintegration processes and to the (anti)neutrino induced deuteron breakup reactions. Specifically, the differential cross section, the photon analyzing power, and the final proton polarization have been calculated for deuteron photodisintegration at photon energies of 30 and 100 MeV. For ${}^3\mathrm{He}$ photodisintegration, predictions for the semi-inclusive and exclusive differential cross sections are presented for photon energies up to 120 MeV. The total cross section is calculated for (anti)neutrino disintegration of the deuteron for (anti)neutrino energies below 200 MeV. Predictions based on the Argonne V18 potential and on an older chiral force with regularization applied in coordinate space are used for comparison. Using the fifth-order chiral nucleon-nucleon potential supplemented with dominant contributions from the sixth order allows us to obtain converged predictions for observables in the investigated reactions. Our results based on the newest semilocal chiral potentials show even smaller cutoff dependence and a somewhat faster convergence for the considered electroweak observables than the previously reported ones with a coordinate-space regulator, which make them a promising tool to study electroweak processes.

Figure 1

The differential cross section $\frac{d^2\sigma }{d\mathrm{\Omega }}$ for the $\gamma +{}^2\mathrm{H}\to p+n$ reaction at the laboratory photon energy $E_{\gamma }=30\mathrm{MeV}$ (top) and $E_{\gamma }=100\mathrm{MeV}$ (bottom) as a function of the proton emission angle ${\theta }_p$ (the angle between the initial photon momentum and the proton momentum) in the center-of-mass frame. The left column shows the dependence of predictions on the order of chiral expansion. The orange solid line with diamonds, the blue solid line with circles, and the green dashed, the red dotted, the black solid, the cyan double-dot-dashed, and the violet dot-dashed curves correspond to the LO, NLO, ${\mathrm{N}}^2\mathrm{LO}, {\mathrm{N}}^3\mathrm{LO}, {\mathrm{N}}^4\mathrm{LO}, {\mathrm{N}}^4\mathrm{LO}+$, and AV18 potential based predictions, respectively. Truncation errors for the different orders of chiral expansion are presented in the middle column. The yellow band shows the truncation errors at NLO, the green band shows the truncation errors at ${\mathrm{N}}^2\mathrm{LO}$, the blue band shows the truncation errors at ${\mathrm{N}}^3\mathrm{LO}$, the red band shows the truncation errors at ${\mathrm{N}}^4\mathrm{LO}$, and finally the black band shows the truncation errors at ${\mathrm{N}}^4{\mathrm{LO}}^{+}$ order. The right column shows the chiral SMS predictions at ${\mathrm{N}}^4\mathrm{LO}$, calculated using different values of the cutoff parameter $\mathrm{\Lambda }$. The cyan double-dot-dashed, the black solid, the green dashed, the red dotted, and the violet dot-dashed curves correspond to $\mathrm{\Lambda }=400$, 450, 500, and 550 MeV and the AV18 based predictions, respectively. For the predictions shown in the left and in the middle columns the regulator value $\mathrm{\Lambda }=450$ MeV is used. The data points at 30 MeV are the same as in Ref. [42] and those at 100 MeV are taken from [42] (open and filled circles, squares) and from [43] (triangles).

Figure 2

The differential cross section $\frac{d^2\sigma }{d\mathrm{\Omega }}$ at $E_{\gamma }=30\mathrm{MeV}$ as a function of the proton emission angle ${\theta }_p$ calculated using the SCS (with $R=0.9$ fm) and the SMS (with $\mathrm{\Lambda }=450\mathrm{MeV}$) chiral potentials. (a) Predictions at higher orders of chiral expansion [${\mathrm{N}}^3\mathrm{LO}, {\mathrm{N}}^4\mathrm{LO}$, and ${\mathrm{N}}^4\mathrm{LO}+$ (for the SMS force only)]. The dashed green, dotted violet, and double-dot-dashed blue lines represent results calculated using the SMS potential up to ${\mathrm{N}}^3\mathrm{LO}, {\mathrm{N}}^4\mathrm{LO}$, and ${\mathrm{N}}^4{\mathrm{LO}}^{+}$, respectively. The solid orange and the dash-dotted red lines are obtained using the SCS potential at ${\mathrm{N}}^3\mathrm{LO}$ and ${\mathrm{N}}^4\mathrm{LO}$, respectively. All data points (open and filled circles) are taken from [42]. (b) SCS (SMS) potential based result at ${\mathrm{N}}^4\mathrm{LO}$ (${\mathrm{N}}^4{\mathrm{LO}}^{+}$) given by the dash-dotted red (double-dash dotted blue) curve and corresponding truncation error represented by the pink (blue) band. Both for the SCS and the SMS forces, predictions and bands overlap.

Figure 3

The same as in Fig. 2 but for $E_{\gamma }=100\mathrm{MeV}$. For the description of curves and bands see Fig. 2. Data are taken from [43] (triangles) and from [42] (open and filled circles and squares).

Figure 4

The relative spread of predictions for the differential cross section for the deuteron photodisintegration reaction at the initial photon energy $E_{\gamma }=30\mathrm{MeV}$. (a) Difference between maximum and minimum values of the differential cross section for all chiral orders used, divided by its average (from LO to ${\mathrm{N}}^4{\mathrm{LO}}^{+}$ for the SMS potential, green solid line; from LO to ${\mathrm{N}}^4\mathrm{LO}$ for the SCS, violet dashed line). (b) Analogous quantity, but measuring the spread with respect to the different cutoff values used (from 400 to 550 MeV for the SMS force and from 0.8 to 1.2 fm for the SCS potential) at fixed chiral order (${\mathrm{N}}^4\mathrm{LO}$). (c) Absolute difference between $\frac{d^2\sigma }{d\mathrm{\Omega }}$ calculated at ${\mathrm{N}}^4\mathrm{LO}$ and ${\mathrm{N}}^3\mathrm{LO}$ for each of two potentials.

Figure 5

Same as in Fig. 4 but for $E_{\gamma }=100\mathrm{MeV}$.

Figure 6

The absolute difference between the values of the differential cross section $\frac{d^2\sigma }{d\mathrm{\Omega }}$ taken at each of two subsequent chiral orders (the one marked on the $x$ axis and the next one) at fixed proton angle ${\theta }_p$ and photon energy: (a) ${\theta }_p={60}^{\circ }, E_{\gamma }=30\mathrm{MeV}$, (b) ${\theta }_p={15}^{\circ }, E_{\gamma }=100\mathrm{MeV}$, and (c) ${\theta }_p={150}^{\circ }, E_{\gamma }=100\mathrm{MeV}$. The violet dashed (the green solid) line represents results obtained using the SCS (SMS) potential with the cutoff parameter $R=0.9$ fm ($\mathrm{\Lambda }=450\mathrm{MeV}$).

Figure 7

The photon analyzing power $A_{\text{X}}$ as a function of the center-of-mass proton detection angle ${\theta }_p$ for the deuteron photodisintegration process at $E_{\gamma }=100\mathrm{MeV}$. (a) Dependence of $A_{\text{X}}$ on the chiral order of the SMS potential at $\mathrm{\Lambda }=450\mathrm{MeV}$. (b) Dependence of $A_{\text{X}}$ on the value of the regularization parameter $\mathrm{\Lambda }$ at ${\mathrm{N}}^4\mathrm{LO}$. (c) Predictions of the SCS and SMS forces together with truncation errors. Lines in panel (a) are as in Fig. 1, those in panel (b) are as in Fig. 1, and those in panel (c) are as in Fig. 3.

Figure 8

Same as in Fig. 7 but for the proton polarization $P_y$.

Figure 9

The total cross section ${\sigma }_{\text{tot}}$ for the ${\nu }_e{+}^2\mathrm{H}\to {\nu }_e+p+n$ reaction as a function of the incoming neutrino energy in the laboratory system. (a) Dependence of ${\sigma }_{\text{tot}}$ on the chiral order at $\mathrm{\Lambda }=450\mathrm{MeV}$. (b) Dependence of ${\sigma }_{\text{tot}}$ on the regulator parameter value at ${\mathrm{N}}^4\mathrm{LO}$. In panel (a) the orange solid line with diamonds, the blue solid line with circles, and the green dashed, red dotted, black solid, cyan double-dot-dashed, and violet dot-dashed curves correspond to the LO, NLO, ${\mathrm{N}}^2\mathrm{LO}, {\mathrm{N}}^3\mathrm{LO}, {\mathrm{N}}^4\mathrm{LO}, {\mathrm{N}}^4\mathrm{LO}+$, and AV18 potential based predictions, respectively. In panel (b) the cyan double-dot-dashed, black solid, green dashed, red dotted, and violet dot-dashed curves represent results with $\mathrm{\Lambda }=400$, 450, 500, and 550 MeV and the AV18 based predictions, respectively.

Figure 10

Same as in Fig. 9 but for the ${\overline{\nu }}_e{+}^2\mathrm{H}\to {\overline{\nu }}_e+p+n$ reaction.

Figure 11

Same as in Fig. 9 but for the ${\overline{\nu }}_e{+}^2\mathrm{H}\to e^{+}+n+n$ reaction.

Figure 12

The semi-inclusive differential cross section $\frac{d^3\sigma }{d{\mathrm{\Omega }}_{p}d{E}_p}$ for the $\gamma +{}^3\mathrm{He}\to p+p+n$ reaction at $E_{\gamma }=120\mathrm{MeV}$ as a function of the outgoing proton energy $E_p$ at different values of the polar angle of the outgoing proton momentum ${\theta }_p$. Top row: Cross-section dependence on the order of chiral expansion (at $\mathrm{\Lambda }=450\mathrm{MeV}$). Bottom row: Dependence on the value of the regularization parameter $\mathrm{\Lambda }$. The curves are as in Fig. 1 but the AV18 prediction is not shown here.

Figure 13

The fivefold differential cross sections $\frac{d^5\sigma }{d{\mathrm{\Omega }}_{1}d{\mathrm{\Omega }}_{2}dS}$ for the complete kinematical configuration with the two protons detected at ${\mathrm{\Theta }}_1={15}^{\circ }, {\mathrm{\Phi }}_1=0^{\circ }, {\mathrm{\Theta }}_2={15}^{\circ }$, and ${\mathrm{\Phi }}_2={180}^{\circ }$ angles for the ${}^3\mathrm{He}$ photodisintegration process at the photon energy $E_{\gamma }=40\mathrm{MeV}$ in the laboratory frame. (a) Dependence on the chiral order (with $\mathrm{\Lambda }=450\mathrm{MeV}$). (b) Results for different regulator values (at ${\mathrm{N}}^4\mathrm{LO}$). Curves are as in Fig. 12.

Figure 14

Same as in Fig. 13 but for $E_{\gamma }=120\mathrm{MeV}$.